The unified transform for the heat equation: II. Non-separable boundary conditions in two dimensions

DOI10.1017/S0956792515000224zbMath1387.35322OpenAlexW2606710676MaRDI QIDQ4594563

Athanassios S. Fokas, Dionyssios Mantzavinos

Publication date: 24 November 2017

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0956792515000224

zbMATH Keywords

initial-boundary value problemstwo-dimensional heat equationunified transform methodnon-separable boundary conditionsoblique Neumann boundary conditions

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Integral representations of solutions to PDEs (35C15) Heat kernel (35K08)

Related Items (7)

Initial-boundary value problem for the one dimensional Thirring model ⋮ Linear evolution equations on the half-line with dynamic boundary conditions ⋮ A Neumann problem for a diffusion equation with \(n\)-dimensional fractional Laplacian ⋮ Generalised Dirichlet to Neumann maps for linear dispersive equations on half-line ⋮ Cubic nonlinear Dirac equation in a quarter plane ⋮ Boundary behavior for the heat equation on the half‐line ⋮ Stochastic diffusion equation with fractional Laplacian on the first quadrant

Cites Work

• On the integrability of linear and nonlinear partial differential equations
• The unified method for the heat equation: I. non-separable boundary conditions and non-local constraints in one dimension
• Synthesis, as Opposed to Separation, of Variables
• The Heat Equation in the Interior of an Equilateral Triangle
• A unified transform method for solving linear and certain nonlinear PDEs
• The modified Helmholtz equation in a semi-strip
• A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line

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